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# Applied and Computational Mathematics

DMS Applied Mathematics Seminar
Dec 01, 2017 02:00 PM
Parker Hall 328

Speaker: Prof. Peter Monk, University of Delaware

Title: Inverse Scattering in a Waveguide

Abstract: I shall present a study of the inverse problem of determining the shape of inclusions in a sound hard waveguide using either frequency or time domain data. Mostly I will focus on the time domain problem and start by proving existence and uniqueness for the forward problem. Then I will derive a numerical method using time domain integral equations. For the inverse problem I will use the Linear Sampling Method due to Colton and Kirsch. After analysis of the time domain inversion scheme, I will provide a few numerical examples.

DMS Applied Mathematics Seminar
Nov 17, 2017 12:30 PM
Parker Hall 246

PLEASE NOTE NEW TIME AND NEW PLACE

Speaker: Dr. Bo Liu, Computer Science Department, AU

Abstract: In this talk, I will present the establishment of a unified general framework for stochastic-gradient-based temporal-difference learning algorithms that use proximal gradient methods. The primal-dual saddle-point formulation is introduced, and state-of-the-art stochastic gradient solvers, such as mirror descent and extragradient are used to design several novel reinforcement learning algorithms. The finite-sample analysis is given along with detailed empirical experiments to demonstrate the effectiveness of the proposed algorithms. Several important extensions, such as control learning, variance reduction, acceleration, and regularization will also be discussed in detail.

DMS Applied Mathematics Seminar
Nov 10, 2017 02:00 PM
Parker Hall 328

Speaker: Hyesuk Lee (Clemson University)

Title: Finite element approximation and analysis for non-Newtonian fluid-structure interaction

Abstract:  Numerical study of non-Newtonian fluid-structure interaction (FSI) provides significant challenges not only due to the strong coupling between the solid and fluid substructures, but also the complexity of fluid model in a moving domain. As a result, advances in numerical study for non-Newtonian FSI have been limited and there are still many open problems in the area.

In this talk both monolithic and decoupling approaches are considered for analytical and numerical studies of fluid-structure interaction problems, where the fluid is governed by a quasi-Newtonian or a viscoelastic fluid model. We will present finite element error estimates for a quasi-Newtonian FSI system and numerical results that show comparisons with a Newtonian FSI system. For a viscoelastic FSI problem we will discuss some issues with the stress boundary condition on the interface and present simulation results with/without interface stress boundary conditions.

DMS Applied Mathematics Seminar
Oct 20, 2017 02:00 PM
Parker Hall 328

We are fortunate to have Professor Ming-Jun Lai <http://alpha.math.uga.edu/%7Emjlai/> from the University of Georgia to speak on the topic of matrix completion <https://en.wikipedia.org/wiki/Matrix_completion>.

Title: On Recent Development of Matrix Completion.

Abstract:  I shall first introduce the research on matrix completion based on Netflix problem. Then I will survey some classic methods based on various approaches. In particular, I will explain some recent approaches based on alternating minimization methods including least squares, steepest descent, and Riemann gradient descent techniques. Finally, I shall explain our method of Alternating Projection Algorithm and present a convergence analysis under some conditions. Linear convergence will be shown under a sufficient condition. I will end my talk with numerical experimental results to demonstrate our method is excellent in completing a matrix of low rank.

DMS Applied Mathematics Seminar
Oct 06, 2017 02:00 PM
Parker Hall 328

Speaker: Prof. Xu Zhang, Mississippi State University

Title: Immersed Finite Element Methods for Interface Problems (Basic idea, Development, Analysis, and Applications)

Abstract: Simulating a multi-scale/multi-physics phenomenon often involves a domain consisting of different materials. This often leads to the so-called interface problems of partial differential equations. Classical finite elements methods can solve interface problems satisfactorily if the mesh is aligned with interfaces; otherwise the convergence could be impaired. Immersed finite element (IFE) methods, on the other hand, allow the interface to be embedded in elements, so that Cartesian meshes can be used for problems with non-trivial interface geometry.

In this talk, we start with an introduction about the basic ideas of IFE methods for the second-order elliptic equation. We will present challenges of conventional IFE methods, and introduce some recent advances in designing more accurate and robust IFE schemes. Both a priori and a posteriori error estimation will be presented. Finally, we will demonstrate how IFE methods can be applied to more complicated interface model problems.

DMS Applied Mathematics Seminar
Sep 22, 2017 02:00 PM
Parker Hall 328

Speaker: Hans-Werner van Wyk

Title: Clenshaw-Curtis Type Rules for Statistical Integrals

Abstract: In statistics, many commonly encountered quantities take the form of density weighted integrals. This talk treats their numerical estimation within the Chebyshev approximation framework. In particular, we discuss how a generic one dimensional density function can be incorporated into the construction of Clenshaw-Curtis type quadrature rules, either through an adjustment of the quadrature weights or by generating a set of quadrature nodes that satisfies the optimal spacing property in terms of the density-weighted uniform error. We consider a variety of density functions, including those that are piecewise continuous, or have unbounded support. The accompanying numerical experiments illustrate the behavior and performance of the resulting quadrature rules and offer a comparison with a variety of existing approaches for estimating density weighted integrals.

Applied Mathematics Seminar/Colloquium Yuesheng Xu
Feb 10, 2017 02:00 PM
Parker Hall 250

Speaker: Professor Yuesheng Xu  (Sun Yat Sen University, China)

Title: Mathematics in Data Science

Abstract: We shall discuss several mathematical problems crucial in data science. They include representation of data, mathematical models of recovering a fact from raw data, matching learning and solving optimization problems in data analysis.

Faculty host:  Yanzhao Cao

Applied Mathematics Seminar
Jan 27, 2017 02:00 PM
Parker Hall 328

Speaker:  Dr. Yi Wang,   Professor and Chair at Auburn University at Montgomery (AUM).

Title: Sparse representation with non-linear Fourier atoms

Abstract: In this talk, we study the sparse representation of a finite energy signal with intrinsic mode functions in a dictionary consisting of non-linear Fourier atoms. Each non-linear Fourier atom is a mono-component with a physically meaningful non-negative instantaneous frequency. The sparse representation is obtained adaptively by an orthogonal matching pursuit using a two-level greedy search. It is demonstrated that the representation has efficient energy decay in error compared to the Fourier expansion and wavelet expansion.

Keywords: sparse representation, non-liner Fourier atom, orthogonal matching pursuit, trust-region-reflective search.

Applied Mathematics Seminar
Nov 11, 2016 02:00 PM
Parker Hall 228

Speaker: Dr. Habib Najm.  Habib is a distinguished member of the technical staff at Sandia National Lab. He is also our affiliated  faulty.

Title: Parameter Estimation with Missing Data

Abstract:  Uncertainty quantification on model predictions, using probabilistic methods, requires a full probabilistic specification, e.g., the joint density, for model parameters. Most commonly, only limited information, such as nominal values and error bar is available on model parameters or relevant data. In this talk, I will discuss means for handling this situation, to allow construction of a joint density on model parameters that is consistent with available information, in the absence of raw data. The method will be illustrated in the context of estimation of the joint density on Arrhenius chemical rate coefficients.
Applied Mathematics Seminar
Oct 28, 2016 02:00 PM
Parker Hall 328

Speaker: Hans-Werner van Wyk

Title: A novel finite difference method for the fractional Laplacian

Abstract: In this talk we discuss a novel finite difference method to discretize the fractional Laplacian operator over a bounded domain. Our approach is based on splitting the hypersingular kernel function in its integral representation into two parts, allowing some of the singularity to be absorbed by the operator’s input function $$u$$. We then approximate the resulting weakly singular integral by a weighted trapezoidal rule. Our method is simple to implement and has a higher accuracy than the existing finite difference approximations. For smooth enough $$u$$ and a judicious choice of the splitting parameter, we obtain second order accuracy, uniformly for any diffusion order.

Last Updated: 09/25/2015